Class 12 Integrals · Short Answer2 Marksdefinite_integration
Class 12 Maths · Integrals · Short Answer #52
Evaluate \(\int_{-\pi/4}^0(1+\tan x)/(1-\tan x)dx\).
✅ Step-by-Step Solution
Final Answer: (ln2)/2
- The tangent addition identity gives (1+tan x)/(1−tan x)=tan(π/4+x).
- The primitive is −ln|cos(π/4+x)|. Its endpoint difference is −ln(1/√2)+ln1=(ln2)/2.
- Therefore the integral equals (ln2)/2.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The tangent addition identity gives (1+tan x)/(1−tan x)=tan(π/4+x).
- [1 mark] The primitive is −ln|cos(π/4+x)|. Its endpoint difference is −ln(1/√2)+ln1=(ln2)/2.
- [0.5 marks] Therefore the integral equals (ln2)/2.
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